WiSe 25/26 Seminar: Goodwillie calculus

Time and place: Thursday 14-16 M101

Program

Goodwillie calculus is a categorification of ordinary calculus where functions are replaced by functors. The basic concept is that of 𝑛-excisive functor, which is the analogue of a polynomial function of degree ≤𝑛. Under suitable conditions, functors between ∞-categories admit 𝑛-excisive approximations, which together form an analogue of the Taylor series called the Goodwillie tower; functors whose Goodwillie tower converges are called analytic. Several basic features of calculus, like the chain rule and the product rule, have counterparts in Goodwillie calculus. The goal of this seminar is to explore these ideas and phenomena.

Date	Speaker	Topic
16.10	Marc Hoyois	Introduction
23.10	Matteo Munafò	Stable categories
30.10	Antonin Milesi	Spectra and stabilization
06.11	Frank van der Top	Construction of the Goodwillie tower
13.11	James Yan	The coefficients of the Goodwillie tower
20.11		The classification of homogeneous functors
27.11	Ou Liu	The stable Dold–Kan correspondence
04.12		Polynomial functors
11.12		Functors from spaces to spectra
18.12	Yiming Wang	Norm maps and the Tate construction
08.01		The derivative
15.01	Zhenming Xu	Higher derivatives
22.01		The derivatives of the identity
29.01	Wenjun Huang	Introduction to the orthogonal calculus
05.02		Introduction to the embedding calculus